EUROPEAN UNIVERSITY INSTITUTE, FLORENCE
DEPARTMENT O F ECONOM ICS
EIII W O R K I N G
EXCHANGE RA
AND THE
Keith
88/345
I am grateful for useful comments and suggestions by Paul de Grauwe and Francesco
Giavazzi. The usual disclaimer applies.
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All rights reserved. No part of this paper may be reproduced in any form without
permission of the author.
(C) Keith Pilbeam Printed in Italy in June 1988 European University Institute
Badia Fiesolana - 50016 San Domenico (Fi) -
Italy
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KEITH PILBEAM
DEPARTMENT OF ECONOMICS ISTITUTO UNIVERSITARIO EUROPEO, BADIA FIESOLANA,
SAN DOMENICO DI FIESOLE, FIRENZE,
ITALIA.
Aprii 1988
EXCHANGE RATE MANAGEMENT AND THE RISK PREMIUM
ABSTRACT
This article uses a standard small country portfolio balance model of exchange rates under the assumption of perfect foresight to
examine the differing effects of foreign exchange market
operations (sterilised and non sterilised) and domestic money
market operations on the exchange rate and domestic interest rate.
It is shown that the operations have differing effects because of
their different impacts on the risk premium. An expression for the
change in the risk premium is endogenously derived from the model
structure. A distinction is made between the direct effect of an operation on the risk premium due to the change in relative asset supplies and the indirect effect due to the change in the exchange
rate induced by the change in relative asset supplies. The net
effect on the risk premium in the case of all three operations is
shown to be ambiguous.
* I am grateful for useful comments and suggestions by Paul De Grauwe and Francesco Giavazzi. The usual disclaimer applies.
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Exchange Rate Management and the Risk Premium
1. Introduction
Exchange rate management involves the conscious use of policy
instruments by the authorities to influence the exchange rate in
their desired direction. The problem facing the authorities is
that they have a number of alternative policy instruments with
which to attempt to manage the exchange rate. More specifically/
there are three commonly employed instruments that a country can
use to influence its exchange rate: An Open Market Operation (0M0)
defined as an increase or decrease in the domestic monetary base
brought about via a purchase or sale of domestic bonds. A Foreign
Exchange Operation (FXO) defined as an increase or decrease in the
domestic monetary base brought about via a purchase or sale of
foreign currency denominated assets. A Sterilised Foreign Exchange
Operation (SFXO) which involves the authorities offsetting the
monetary base implications of a purchase or sale of foreign assets
via a sale or purchase of domestic bonds. Distinguishing between
OMO's FXO's and SFXO's is clearly important for policy makers who
have available these three alternative instruments for managing
the exchange rate.
In the monetary models of exchange rate determination be they
of the "sticky price" Dornbusch (1976), Frankel (1979) type or the
all prices "fully flexible" Frenkel (1976), Mussa (1976), Bilson
(1978) type, the authorities can only influence the exchange rate
by altering the supply of money in relation to the demand for
money. In the monetary models domestic and foreign bonds are
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2-assumed to be perfect substitutes, hence, there is no difference
in the exchange rate effects between an 0M0 and FXO that change
the money stock by equivalent amounts. The monetary models by
assuming perfect substitutability invoke the assumption of
uncovered interest rate parity, that is:
r - rf = Es
Where: r = nominal domestic interest rate,
rf = nominal foreign interest rate.
Es = expected rate of depreciation of the domestic currency
In the monetary models of exchange rate determination since a SFXO
does not alter the relative money stocks it cannot have any
exchange rate effects. A SFXO is an exchange of domestic for
foreign bonds which are assumed by the monetary models to be
perfect substitutes it follows that a SFXO cannot exert any
exchange rate effects.
The portfolio balance model of exchange rate determination was
originally developed by Branson (1976) and Kouri (1976) and later
extended by Girton and Henderson (1977), Obstfeld (1980), Allen
and Kenen (1980), Branson (1977, 1984), Kouri (1983) and Frankel
(1983 and 1984). In the portfolio balance approach the authorities
can break up the uncovered interest parity condition by
influencing a so called risk premium:
r - rf = Es + RP
Where the risk premium depends for its existence upon the
fulfillment of all three of the following conditions (see Frankel
1979b and 1986) Firstly, there are differences in the perceived
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risks between domestic and foreign bonds - the essence of a risky
asset being that its expected real rate of return is uncertain. If
there are no perceived differences in risks then with perfect
capital mobility they must be perfect substitutes. Secondly, there
has to be risk aversion on the part of economic agents to the
perceived differences in risk - the principle of risk aversion is
that investors will only be prepared to take on increased risk if
there is a sufficient increase in expected real returns to
compensate. Finally, there must be a difference between the risk
minimizing portfolio and the actual portfolio forced at market
clearing prices into the investors portfolios. If all three of
these conditions are fulfilled then the uncovered interest parity
condition will not hold due to the existence of a risk premium
which represents the compensation required by private agents for
accepting risk exposure above the minimum possible.
The attractiveness of the portfolio balance approach is
threefold: (i) it allows for different relative asset supplies
other than money to influence the exchange rate and hence OMO's,
FXO's and SFXO's which alter relative asset supplies in different
ways have differing exchange rate and interest rate effects (ii)
it introduces a role for the current account to influence the
exchange rate because a current account surplus represents an
accumulation of foreign assets by domestic residents (iii) it can
admit the monetary model as a special case of perfect
substitutability between domestic and foreign bonds.
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4-In this paper, a standard small country portfolio balance
model under the assumption of perfect foresight is used to examine
the differing exchange rate and interest rate implications of
FXO's, OMO's and SFXO's. The model outlined follows the portfolio
balance specification as developed by William Branson (1976, 1977
and 1984). The contribution of the paper is that it is shown that
the different exchange rate and interest effects of the three
operations are due to the risk premium an expression for which is
endogenously derived from the model structure. The only other
paper to derive such an expression for the risk premium from the
portfolio balance model is contained in Dooley and Isard (1983)
but they derive their expression with static exchange rate
expectations so that the expected exchange rate component of the
risk premium is not explicitly dealt with. This paper deals
explicitly with both the interest rate and exchange rate component
of the risk premium. The incorporation of the exchange rate effect
on the risk premium is shown to be important when evaluating the
impact of the operations on the risk premium.
The paper is set out as follows: Section two sketches the
model, derives the two schedules crucial to the dynamics of the
model and examines the conditions necessary for stability. Section
three analyses the differing exchange rate effects of the
operations. Section four examines the effects of the three
operations on the risk premium. The final section points to the
limitations of the portfolio balance model and extensions for
future research.
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2. The Model
There are assumed to be three assets that are held in the
portfolios of the private agents and the authorities: Domestic
monetary base, M. Domestic bonds denominated only in the domestic
currency, B. Foreign bonds denominated only in the foreign
currency, F.
Domestic bonds may be held by either domestic agents or the
authorities. Thus, we may denote the net supply of domestic bonds
which is assumed to be fixed [1] as:
B = Bp + Ba (1)
Where: B is the fixed net supply of domestic bonds Bp is the domestic bond holdings of private agents Ba is the domestic bond holdings of the authorities
Similarly, the country's net holding of foreign bonds is held by
private agents and the authorities which we assume in our analysis
to be positive in both cases and equal to the summation of
previous current account surpluses [2]. Unlike the stock of
domestic bonds the holdings of foreign assets may be increased or
decreased over time via a current account surplus or deficit.
Thus, we have:
F = Fp + Fa (2)
Where: F is the net holdings of foreign bonds by the country Fp is the foreign bond holdings of private agents Fa is the stock of foreign bonds held by the authorities
The domestic monetary base liability of the authorities is
equivalent to their assets so that:
M = Ba + sFa (3)
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6-Where s is the exchange rate defined as domestic currency units per unit of foreign currency.
For simplicity it is assumed that capital gains or losses to the
authorities as a result of exchange rate changes do not affect the
monetary base.
Total private financial wealth [3] at any point in time is given
by the identity:
W = M + Bp + sFp (4)
The demand to hold money by the private sector is inversely
related to the domestic interest rate, inversely related to the
expected rate of return on foreign bonds and positively to
domestic income. This yields:
M = m(r, rf+s, Y, W) m <0, m.<0, m >0 and m >0 (5)
' r s y w
Where: r = domestic nominal interest rate
rf = fixed foreign interest rate
s = expected/actual rate of depreciation of the domestic
currency
Y = domestic nominal income
m ,m., m and m are partial derivatives
r s y w
The demand to hold domestic bonds as a proportion of private
wealth is positively related to the domestic interest rate,
inversely related to the expected rate of return on foreign assets
and inversely related to domestic nominal income. This yields:
Bp = b(r, rf+s, Y, W) b >0, b.<0, b <0 and b >0 (6)
^ ' r s y w
Where: b , b., b and b are partial derivatives,
r s y w
The demand to hold foreign bonds as a proportion of total wealth
is inversely related to the domestic interest rate, positively
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related to the expected rate of return from holding foreign bonds
and inversely related to domestic nominal income. This yields:
sFp = f(r, rf+s, Y, W) f <0, f.>0, f <0 and f >0 (7)
* r s y w
Where: f , f., f and f are partial derivatives,
r s y w
The balance sheet constraint is given by the identity:
m + b + f = 1 Balance Sheet Constraint
W W W
The balance sheet identity is coupled with the assumption that
assets are gross substitutes implying the following constraints on
the partial derivatives:
m + b + f = 0
r r r
m. + b. + f . = 0
s s s
The current account balance is crucial to the dynamics of the
system because the current account surplus gives the rate of
accumulation of foreign assets. That is:
C = dFp = fp = T + rf (Fp + Fa) (8)
dt
Where: C = current account surplus
T = the trade balance in foreign currency
The current account is made up of two components: the revenue from
net exports (the trade balance) and interest rate receipts from
net holdings of foreign assets. One of the long run stationary
state equilibrium conditions in this zero growth model is that the
current account balance is zero.
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Net exports are assumed to be a positive function of the real
exchange rate
T = T(s/Pd) Ts>0 (9)
Where: Pd is the domestic price level Ts is the partial derivative
The assumption that net exports are a positive function of the
real exchange rate is quite strong because it rules out the well
known possibility that there may be an initial J-curve effect on
the trade balance, the assumption implies that the Marshall-Lerner
condition always holds.
It is assumed that foreign exchange market participants form their
expectations rationally and in fact possess perfect foresight with
respect to the exchange rate. This assumption means that we can
interchange the expected rate of depreciation with the actual rate
(ie Es = s ) .
We can by taking two equations from (5) to (7) and substituting
the wealth definition from equation (4) and utilising the
assumption of perfect foresight derive s = 0 and £p = 0 schedules
as functions of M, B and sFp. The resulting s=0 and £p=0 equations
can then be represented on a phase diagram in the s, Fp plane. -
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The s = 0 Schedule
In appendix 1 it is shown that by simultaneously solving the
domestic money market equation (5) with the foreign asset market
equation (7) the s = 0 schedule has a negative slope in the s, Fp
plane given by the expression:
ds -s
dFp s=0 Fp
Since the elasticity of the s=0 schedule is given by the
expression Fpds/sdFp = -1, the s=0 schedule must be a rectangular
hyperbola in the s, Fp plane.
The Fp = 0 Schedule
In appendix 1, it is shown that by taking equation (8) the Pp = 0
schedule has a negative slope in the s, Fp plane given by:
ds . = -rf dFp Fp=0 Ts
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10-Equilibrium and Stability of the Model
The model is in equilibrium when the Ép = 0 schedule intersects
the s = 0 schedule. Since the s = 0 schedule is a rectangular
hyperbola and the Ép = 0 schedule has a negative slope the model
has two possible equilibrium solutions as depicted below:
Figure 1: Equilibrium of the Model
FP
The fact that the model has two possible equilibrium solution is
disturbing because as we see below only the linear approximation
around point A has a unique saddle path leading to equilibrium.
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Figure 2: Linear Approximation of the Model
Figure A Figure B
As we can see from the phase diagrams only around point A is
there a unique saddle path S1S1 leading to equilibrium under the
assumption of perfect foresight, at point B all paths lead away
from equilibrium [4]. The condition for the model to exhibit a
unique saddle path leading to equilibrium is that the s schedule
is steeper than the £p schedule. The slope of the s schedule is
given by -s/Fp and the slope of the £p schedule is given by the
term -rf/Ts, thus the condition for a saddle path equilibrium is
that s Ts > rf Fp. This condition is assumed to hold in what
follows to ensure an economic analysis that tends to equilibrium.
This stability condition is formally proven in appendix two.
The economic reasoning behind the necessary stability
condition is easy to follow: When there is a current account
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12-surplus there will be an appreciation of the exchange rate and
with it a fall in net exports. However, the current account
surplus also implies an accumulation of foreign assets and with it
increased interest rate receipts which improve the current account
surplus. Consequently, for the appreciation of the exchange rate
to reduce the current account surplus it is necessary that the
fall in net exports exceed the increased interest rate receipts.
In addition, since there is only a unique saddle path leading
to equilibrium it is assumed that following the introduction of a
disturbance the economy jumps onto the unique saddle path that
leads to equilibrium.
3. The Effects of FXO's OMO's and SFXO's.
With an expansionary FXO, the authorities purchase foreign bonds
from the private sector with newly created monetary base, that is,
dM = -sdFp = sdFa. There will be an upward shift of the s = 0
schedule given by the expression:
dM s=0 [f m + m - m f ]Fp
r w r r w
With an expansionary OMO, the authorities increase the private
sectors holdings of money and decrease their holdings of domestic
bonds by an equivalent amount, that is, dM = - dBp = dBa. In this
case, there is again an upwards shift of the s schedule given by
the expression: f r [ f m + m - m r w r r f ]Fp ds dM s = 0
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W-ith a sterilised -interven-tion in the foreign exchange market
there is a purchase of foreign assets with domestic money base and
the an equivalent sale of domestic bonds so as to leave the money
base unchanged that is, -sdFp = dBp, it is tantermount to the
authorities altering the currency composition of bonds held in
private portfolios. In this case there will be an upward shift of
the s schedule given by the expression:
dBp s=0 [f m + m - m f ] F p
r r w r r w
Which upon observation is seen to be simply the expression for an
FXO less an 0M0.
The effect of the upward shift of the s schedule is illustrated
below:
Figure 3: The Effects of a Shift in the s Schedule.
4 Fp
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14-Following an operation of whatever sort, there is an upward shift
of the s schedule. There is a jump depreciation of the exchange
rate onto the new saddle path S2S2 from si to s2. The jump
depreciation is required to restore instantaneous asset market
equilibrium to asset holders portfolios since an operation of
whatever sort creates an excess demand for foreign assets that can
only be satisfied in the short run by a depreciation of the
domestic currency.
The initial depreciation implies that there is a depreciation
of the real exchange rate. The result is that the current account
moves into surplus, the surplus leads to increased private sector
holdings of foreign assets which in turn results in an increased
demand for domestic assets with a resulting appreciation of the
domestic currency. The economy thus moves along the saddle path
S2S2 until new long run equilibrium is reached at exchange rate s.
During the transition to long run equilibrium the economy
experiences a current account surplus and an appreciating
currency, Kouri (1983) labels such a link between the current
account and the exchange rate as the "acceleration hypothesis."
One of the features of the model is that it is long run non
neutral with respect to the real exchange rate. This is because
the current account surplus that follows an operation results in
an accumulation of foreign assets and an accompanying increase in
the contribution of interest rate receipts from the holding of
foreign assets on the service component of the current account. As
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such, it is necessary for the real exchange rate to have
appreciated in the long run equilibrium so that there is a
deterioration of the trade account to offset the improvement in
the service account to ensure that the current account is restored
to balance in the long run [5].
From the expressions for the upward shift of the s schedule we
can see that the shift is greater in the case of an FXO, this
implies that the saddle path following an FXO lies above that
following an 0M0 so that the initial jump in the exchange rate is
greater following an FXO than in the case of an OMO. The economic
reasoning for this result is that an FXO leads to a initial fail
in private agents holdings of foreign assets while an OMO does
not, consequently an FXO creates an even greater excess demand for
foreign bonds than an OMO, requiring that the initial jump in the
exchange rate has to be greater than for an OMO. Only when
domestic and foreign bonds are perfect substitutes so that -f^-^JO
do the effects of an OMO and FXO on the initial jump in the
exchange rate become identical.
In the case of a SFXO, it is seen that the operation has a
relatively weaker effect on the nominal exchange rate than a FXO
because the shift of the s schedule is less than in the case of an
FXO. This ensures that the new saddle path following a SFXO must
lie below that of a FXO which guarantees that the initial jump in
the exchange rate is less than that which follows a FXO. As such,
a SFXO is a relatively ineffective means of influencing the
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16-exchange rate. In the limiting case where domestic and foreign
bonds are perfect substitutes (b = -f r r r a SFXO will have no
exchange rate effects.
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4. Analysing the Effects on the Risk Premium
The essential difference between the monetarist approach to
exchange rate determination and the portfolio balance approach is
that the latter breaks up the uncovered interest rate parity
condition by introducing a risk premium. That is:
r - rf = Es + RP
Where: RP is the risk premium on the domestic currency assets.
It therefore follows that under the assumption of perfect
foresight (Es = s) that:
dr - drf = ds + dRP
Since in the model the foreign interest rate is assumed to be
fixed (drf=0), I can rearrange the above to yield:
dRP = dr - ds
Around the neighbourhood of the stationary equilibrium ds = s and
appendix one derives an expression for dr. This means that it is
possible to derive from the structure of the portfolio balance
model itself an expression for the change in the risk premium
which is reported below:
b . + b. m ] dM + [ £ - f m + m f :| dM s w s s w r r w w + [m. - m. h + b . m ] dB + [ -f m + m f '| dB s s w s w r w i w + [ -m. b + b . m ] s dFp + [-£ m - m + m f '| e dFp s w s w + [ -m. b + b. m ] Fp ds + r - f m - m + m f ■| Fp ds s w s w r w c r w [m. b r - b .s m ]r [ f . m s r - fr m. 's 'i
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18-Following an 0M0 the effect on the risk premium is given by
dRPomo = [- b. - m . ] dM + [-m. b + b. m ]Fp ds s s s w s w [m. b - b. m ] s r s r + [f ] dM + [-f m - m + m f ]Fp ds r r w r r w ^ [ f . m - f m . ] s r r s
Following an FXO the effect on the risk premium is given by
dRPfxo = [—b .] dM + [-m. b + b. m ]Fp ds s s w s w [m. b - b. m ] s r s r + [f + m ] dM + [-f m - m + m f ]Fp ds r r r r r r w r [f . m - f m.] s r r s
Following an SFXO the effect on the risk premium is given by
dRPsfxo = [m.] dB + [-m. b + b. m ]Fp ds s_____ s w s r * [m. b - b. m ] s r s r + [m ] dB + [-f m - m + m f ]Fp ds r r w r r w ( f . m - f m . ] s r r s
These results for the various operations are summarised in the
table below. In so doing, I distinguish between the direct effect
of the operation on the risk premium and the indirect effect. The
direct effect results from the change in relative asset supplies
and the indirect effect results from the change in the exchange
rate induced by the change in relative asset supplies. Both the
domestic interest rate and change in the expected depreciation of
the currency may be divided up into direct and indirect effects.
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Effects on the Risk Premium dr -ds dRP Type of operation D I N D I N D I N OMO dM = - dBp - - - + - + ? - ? FXO dM = -sdFp - - - + - + ? - ? SFXO dBp= -sdFp + _ 7 + + + - ?
D - direct effect I - indirect effect N - net effect (D+I)
[dM, dB, dFp] [Fp ds ]
Some explanation <Df the results reported above is necessary:
the case of an OMO and FXO the direct effect of the increase
the money supply is to depress the domestic interest rate, this
effect is more pronounced in the case of an OMO because the
operation reduces private agents holdings of domestic bonds. In
the case of an SFXO, however, the direct effect is to raise the
domestic interest rate, this is because the operation increases
private agents holdings of domestic bonds relative to the other
two assets. In all three cases, the indirect effect on the
domestic interest rate is negative as the depreciation increases
private agents.wealth leading to an increased demand for domestic
bonds [6].
With regard to the exchange rate effect, the direct effect of
the operations is to lead to an expected appreciation of the
currency as the operations increase the relative holdings of
domestic assets or in the case of an OMO the proportion of non
interest earning money to bonds. The indirect effect of the
depreciation, however, works in the opposite direction because the
depreciation has the effect of of increasing relative holdings of
foreign assets requiring an expected depreciation of the domestic
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-
20-currency. We know, however, that if the economy jumps onto the
unique stable saddle path the former effect outweighs the latter
so that there is an expected appreciation of the domestic
currency.
As can be seen, unless we impose constraints upon the various
parameters, it is not possible to evaluate the net effect on the
risk premium of the various operations. The source of the
ambiguity derives from the fact that the depreciation following an
operation of whatever sort revalues private holdings of foreign
bonds and with it raises domestic wealth which leaves it unclear
whether or not the stock of domestic bonds and money rise or fall
as a proportion of wealth. That is:
RP = RP (M/W, Bp/W) RP1>0 RP2>0.
In the case of an OMO it is clear the ratio Bp/W declines,
however, it is unclear what happens to the M/W ratio. With an FXO
while the ratio Bp/W falls it is unclear whether the ratio M/W
rises or falls. While in the case of an SFXO it is unclear whether
the ratio Bp/W rises or falls while the M/W ratio falls.
The above explanation may help account for the difficulty that
some authors such as Frankel (1982) and Rogoff (1984) have had in
explaining the empirical behaviour of the risk premium in terms of
only relative asset supplies. This is because the risk premium may
rise or fall following an operation of whatever sort to manage the
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exchange rate due to the exchange rate effect induced by the
change in relative asset supplies.
5. Conclusions
In this paper, I have argued that the distinguishing feature of
the portfolio balance model is that it breaks up the uncovered
interest rate parity condition by the introduction of a risk
premium. I have derived from the model structure itself an
equation for the change in the risk premium. This contribution is
of significance for two reasons: Firstly, the change in the risk
premium is affected by changes in all the asset supplies depicted
in the model including the domestic money supply, this suggests
that existing research which typically analyses the risk premium
in relation to only two assets - domestic and foreign bonds, needs
to be extended to explicitly include changes in the money stock.
Secondly, due to the wealth effects resulting from a change in the
exchange rate induced by changes in relative asset supplies,
it is not possible to identify unambiguous effects on the risk
premium. Whatever, one cannot analyse exchange rate management
without analysing the risk premium.
One fairly strong conclusion that emerges from the portfolio
balance model is that a given change in the money stock has a more
powerful effect on the exchange rate when carried out by a
purchase of foreign assets than when achieved via a purchase of
domestic assets. It is only in the limiting case when domestic and
foreign bonds are perfect substitutes that the effects become
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22-identical. This is an important result because it at least
provides a rationale for the observed interventions of authorities
in foreign exchange markets. Another clear result that follows is
that it is only by assuming that domestic and foreign bonds are
imperfect substitutes that a SFXO can exert exchange rate effects
through a portfolio balance channel. It has been shown that a SFXO
will have a relatively weaker effect on the exchange rate than an
FXO.
Since the risk premium is a function of perceived risks the
portfolio balance model may be subject to the Lucas critique. The
portfolio balance model as we have seen assumes that the domestic
authorities can manipulate the risk premium by changing relative
asset supplies and that this gives them the scope to pursue an
SFXO. However, it may be the case that the operation itself alters
the level of perceived risks in an unpredictable fashion so that
an operation that was intended to reduce the risk premium ends up
increasing it leading to a reversal of the results of the model.
Clearly, how the various operations affect risk perceptions is an
area that merits closer attention.
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Footnotes
[1] In order to assume that the supply is fixed it is necessary to
assume in the following analysis that the budget is
continuously balanced. For an excellent analysis of the
Portfolio balance model with budget deficits see Penati (1986).
[2] It has been suggested by some authors that a negative net
foreign asset position may imply instability in portfolio
balance models. However, as Branson and Henderson (1985)
demonstrate this is not the case if one utilises the
assumption of rational expectations in the foreign exchange market. The instability problem can arise only if one assumes
non rational expectations such as static or regressive
expectation mechanisms.
[3] The portfolio balance model makes the assumption that both domestic and foreign bonds are regarded as net wealth by
private agents. However, Barro (1974) argues that since
private agents realise that a government financed bond deficit will mean increased future tax liabilities then private agents do not regard bonds as net wealth.
[4] The fact that there is is only a single saddle path that leads to equilibrium is a typical feature of rational expectations models.
[5] Claassen (1983) derives a similar result in a quantity
theoretical two country comparative static model. Following a monetary expansion the current account of the expanding country goes into surplus due to the real depreciation of its
currency. In the final equilibrium it is necessary for there
to be a deterioration of the trade account of the country so as to offset the improved interest rate receipts from the
holdings of foreign assets. This deterioration is brought
about via a real appreciation of the domestic currency and the wealth effect of the accumulation of foreign assets on import
expend i ture.
[6] The effect of an increase in private agents wealth is shown in appendix one to be ambiguous. The ambiguity arises from the
fact that an increase in foreign bond holdings leads to an
increased demand for both domestic money and bonds and the
domestic interest rate will have to adjust to satisfy the
relative demands in these two markets. In the analysis the
domestic interest rate is assumed to fall as agents demand
relatively more bonds than money in response to the increase
in wealth.
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24-Appendix 1; Solving for s = 0 , ftp = 0 and dr.
The s = 0 schedule
Taking the total differential of equation (5) and using the fact
that in the neighbourhood of the stationary state ds=s (Branson
and Henderson 1985 p.760) yields:
dM = m dr + m. s + m dW (10)
r s w
Taking the total differential of equation (7) yields:
dsFp = f dr + f. s + f dW (11) r s w From equation (10) dr = dM - nu s - m^ dW m r From equation (11) dr = dsFp - f. s - f^ dW f So that dM - m. s - m dW = dsFp - f. s - f dW ______s______ w ____ s______w m f r r
Multiplying through both sides by (f^ m^), and using the fact that
dW = dM + dB + dsFp and dsFp = Fp ds + s dFp and rearranging, I
obtain: + f m - m f ] r w r w [ f m - m £ ] r w r w m + m - m £ ] s w r r w m + m - m £ ]Fp w r r [ f . m s r - fr m. ]s [f [f dB dFp ds (12)
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The ftp = 0 Schedule
In the analysis it is assumed that fa = 0 so by taking the total
differential of equation (8) and using the fact that in the
neighbourhood of the stationary state dfp=fp, I obtain:
fp = Ts ds + rf dFp (13)
Solving for the Domestic Interest Rate
The domestic interest rate has to adjust to clear the domestic
money and bonds market. Taking the total differential of equation
(5) yields:
dM = m dr + m. s + m dW
r s w
Taking the total differential of equation (6) yields
dB = b dr + b. s + b dW r s w Thus dM - m dr - m dW = s and dB - b dr - m dW = s ______r_______ w r w m. b. s s So that dM - m dr - m dW = dB - b dr - b dW r w r w m . b. s s
Multiplying through by (m. b^), splitting up the expression dW and
rearranging yields: [ -m. b s w b.3 + b.s mwi dM + [m. - m. s s bw + b.5 mwi dB + [ -nu b w + b .s mw]s dFp + [ -nu b w + b. mw]Fp ds [m. s br - b .s mr]
From the above expression, it is evident that an increase in the
money stock depresses the domestic interest rate and an increase
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26-in the supply of domestic bonds held by private agents requires a
rise in the domestic interest rate. The wealth effect of an
increase in wealth either via an increased private holdings of
foreign bonds or a depreciation of the exchange rate is ambiguous,
In the analysis, I assume that |-m. b |>|b. m |, so that an
s w s w
increase in wealth by raising the demand for domestic bonds
depresses the domestic interest rate.
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Appendix Two;
Eigenvalues, Stability, Initial Conditions and Rates of Change
In this appendix, I derive the eigenvalues of the system,
conditions necessary for stability, the initial conditions and
expressions for the expected rates of change of the exchange rate
and rate of accumulation of foreign assets during the transition
to the steady state.
The two dynamic variables linearised around the steady state are
expressed in matrix form as:
s [f m + m - m f ] F p [f m + m - m f ] s
r w r r w r w r r w s - s
[ f . m - f m . ]
s r r s [ f .s r m - f m. ]r s
/p_ Ts rf Fp - Fp
As is well known, the roots of the above matrix can be found by
using the trace and determinant. The two roots are given by:
•A*, Ai= Fp X + rf - X + rf]^- 4 [ Fp X rf - s X Ts] 2 Where: X = [ f m + m - m f ] > 0 r w____ r____ r w [ f . m - f m . ] s r r s
Thus, providing that s Ts > rf Fp the above system will produce a
saddle point equilibrium with one negative and one positive
characteristic root given by-4< and -A^respect ively.
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28-Time Paths
The general solution for the time path of the two variables is
given by: X t „ .Ait s(t) = c A e + c., B e + s . o 1 Ai t Ait -Fp(t) = Cq e + e + Fp.
Where: e is the natural number 2.718...
c and c, are determined by the initial conditions,
o 1
0
andjBjare the eigenvectors.I d .
A; and As, are the negative and positive characteristic roots respectively. Initial Conditions At time t = 0 (s - s) = c A o (Fp - Fp) = Cq
Therefore A gives the slope of the saddle path.
At the steady state, we know s = Fp = 0. Only the negative
characteristic root produces a unique path leading to equilibrium
so we have to set c^=0. Next, we find the value of the eigenvalue
Fp X - A* s X A 0
Ts rf - A 1 _0_
Therefore A = /A» - rf < 0 the saddle path has a negative slope.
Ts
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Fp(0) = c q + Fp so that = Fp(0) - Fp Hence: s(0) - s = [Fp(0) - Fp]
[X\
- rf] Ts Rates of Change i a Ait s = c A. A e o and ^p = c A» eoThe above is nothing more than a statement of the acceleration
hypothesis, when there is an accumulation of foreign assets due to
a current account surplus the exchange rate appreciates during the
transition to equilibrium.
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3 0
-References
Allen P.R. and Kenen P.B. Asset Markets, Exchange Rates, and Economic Integration. Cambridge University Press, Cambridge, 1980.
Argy V. Exchange Rate Management in Theory and Practice. Princeton Studies in International Finance No 50, 1982.
Barr D.G. "Exchange Rate Overshooting and Monetary Policy in an Open Economy Portfolio Balance Model." Centre for Labour Studies, London School of Economics, Discussion Paper No 201, 1984.
Barro R.J. "Are Government Bonds Net Wealth ?" Journal of Political Economy, Vol 82, pp.1095-117, 1974.
Blundell-Wignall A. and Masson P.R. "Exchange Rate Dynamics and Intervention Rules." IMF Staff Papers, Vol 32, pp.132-59, 1985.
Branson W.H. Asset Markets and Relative Prices in Exchange Rate
Determination. Institute for International Economic Studies,
Seminar Paper No 66, Stockholm, 1976.
Branson W.H., Hattunen H. and Masson P. "Exchange Rates in the
Short Run: The Dollar-Deutschemark Rate." European Economic
Review, Vol 10, pp.303-24, 1977.
Branson W.H. "A Model of Exchange Rate Determination with Policy Reaction: Evidence from Monthly Data." In Malgrange P. and Muet
P .A. Contemporary Macroeconomic Modelling. Basil Blackwell,
Oxford, 1984.
Branson W.H. and Henderson D.W. "The Specification and Influence of Asset Markets." In Kenen P.B. and Jones R.W. Handbook of International Economics, Vol II. Elsevier, Amsterdam, 1985.
Dooley M. "An Analysis of Exchange Market Intervention of Industrial and Developing Countries." IMF Staff Papers, Vol 29, pp.233-69, 1981.
Dooley M. and Isard P. "A Portfolio Balance Rational Expectations Model of the Dollar-Mark Exchange Rate." Journal of International Economics, Vol 12, pp.257-76, 1982.
Dooley M. and Isard P. "The Portfolio-Balance Model of Exchange
Rates and Some Structural Estimates of the Risk Premium." IMF
Staff Papers, Vol 30, pp.683-702, 1983.
Dornbusch R. "Expectations and Exchange Rate Dynamics." Journal of Political Economy, Vol 84, pp.1161-76, 1976.
Dornbusch R. and Fischer S. "Exchange Rates and the Current Account." American Economic Review, Vol 70, pp.960-71, 1980.
©
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Author(s).
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Frankel J.A. "On the Mark: A Theory of Floating Exchange Rates Based on Real Interest Rate Differentials." American Economic Review, Vol 69, pp.610-22, 1979a.
Frankel J.A. "The Diversifiability of Exchange Risk." Journal of International Economics, Vol 9, pp.379-93, 1979b.
Frankel J.A. "A Test of Perfect Substitutability in the Foreign
Exchange Market." Southern Economic Journal, Vol 49, pp. 406-16,
1982.
Frankel J.A. "Monetary and Portfolio Balance Models of Exchange
Rate Determination." In Bhandari J.S. and Putnam B.H. Economic
Interdependence and Flexible Exchange Rates. MIT Press, Cambridge Mass, 1983.
Frankel J.A. "Tests of Monetary and Portfolio Balance Models of
Exchange Rate Determination." In Bilson J.F.O. and Marston R.C.
Exchange Rate Theory and Practice. University of Chicago Press, Chicago, 1984.
Frenkel J.A. "A Monetary Approach to the Exchange Rate: Doctrinal
Aspects and Empirical Evidence." Scandanavian Journal of
Economics. Vol 78, pp.169-91, 1976.
Genberg H. "The Effects of Central Bank Intervention in the
Foreign Exchange Market." IMF Staff Papers, Vol 28, pp.451-76,
1981.
Girton L. and Henderson D.W. "Central Bank Operations in Foreign and Domestic Assets Under Fixed and Flexible Exchange Rates." In Clark P.B., Logue D.E. and Sweeny R.J. The Effects of Exchange Rate Adjustment. Government Printing Office, Washington, 1977.
Henderson D.W. and Rogoff K. "Negative Net Foreign Asset Positions and Stability in a World Portfolio Balance Model." Journal of International Economics, Vol 13, pp.85-104, 1982.
Kenen P.B. "Effects of Intervention and Sterilization in the Short
Run and the Long Run." In Cooper R.N. Kenen P.B. Macedo J.B. and
Ypersele J.V. The International Monetary System Under Flexible
Exchange Rates. Ballinger, Cambridge Mass, 1982.
Kouri P.J.K. "Capital Flows and the Dynamics of the Exchange Rate." Institute for International Economic Studies, Seminar Paper No 67, Stockholm, 1976.
Kouri P.J.K. "Balance of Payments and the Foreign Exchange Market: A Dynamic Partial Equilibrium Model." In Bhandari J.S. and Putnam
B.H. Economic Interdependence and Flexible Exchange Rates. MIT
Press, Cambridge Mass, 1983.
Lucas R.E. Jnr. "Econometric Policy Evaluations: A Critique." In Brunner K. and Meltzer A.H. The Phillips Curve and Labour Markets.
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3 2
-Car neg ie-Roches ter Conference Series on Public Policy No 1, North-
Holland, Amsterdam, pp.19-46, 1976.
Mussa M. "The Exchange Rate, the Balance of Payments, and Monetary
and Fiscal Policy Under a Regime of Controlled Floating."
Scandanavian Journal of Economics, Vol 78, pp.229-48, 1976.
Mussa M. "The Theory of Exchange Rate Determination." In Bilson
J.F.O. and Marston R.C. Exchange Rate Theory and Practice.
University of Chicago Press, Chicago, 1984.
Obstfeld M. "Imperfect Asset Substitutability and Monetary Policy Under Fixed Exchange Rates." Journal of International Economics, Vol 10, pp.177-200, 1980.
Obstfeld M. "Can We Sterilize? Theory and Evidence." American Economic Review Papers and Proceedings, pp.45-50, 1982.
Penati A. "Budget Deficit, External Official Borrowing and Sterilized Intervention Policy in Foreign Exchange Markets." Journal of International Money and Finance, Vol 5, pp.99-113, 1986.
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